Multi-hadron-state contamination in nucleon observables from chiral perturbation theory

TL;DR

This paper uses baryon chiral perturbation theory to estimate how multi-pion states contaminate nucleon observable calculations in lattice QCD, revealing a significant overestimation at typical source-sink separations.

Contribution

It demonstrates how ChPT can quantitatively evaluate multi-pion contamination in nucleon observables from lattice simulations, providing guidance for future lattice calculations.

Findings

Multi-pion states cause 5-10% overestimation of nucleon charges and moments.

Larger source-sink separations (>2 fm) are needed for high-precision lattice results.

ChPT predictions align with existing lattice data, supporting their validity.

Abstract

Multi-particle states with additional pions are expected to be a non-negligible source of the excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory (ChPT) can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Results to leading order are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions: the average quark momentum fraction, the helicity and the transversity moment. Taking into account experimental and phenomenological results for the charges and moments the impact of the nucleon-pion-states on lattice estimates for these observables can be estimated. The nucleon-pion-state contribution leads to an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5-10% level for source-sink separations of about 2 fm. Existing lattice data is not in conflict with the ChPT predictions, but the comparison suggests that significantly larger source-sink separations are needed to compute the charges and moments with few-percent precision.